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تسجيل مستخدم جديدZero Distribution of Hermite-Pade Polynomials and Convergence Properties of Hermite Approximants for Multivalued Analytic Functions
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In the paper, we propose two new conjectures about the convergence of Hermite Approximants of multivalued analytic functions of Laguerre class ${mathscr L}$. The conjectures are based in part on the numerical experiments, made recently by the authors in [26] and [27].
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We consider the problem of zero distribution of the first kind Hermite--Pade polynomials associated with a vector function $vec f = (f_1, dots, f_s)$ whose components $f_k$ are functions with a finite number of branch points in plane. We assume that
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In this paper are discussed the results of new numerical experiments on zero distribution of type I Hermite-Pade polynomials of order $n=200$ for three different collections of three functions $[1,f_1,f_2]$. These results are obtained by the authors
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We propose an algorithm for producing Hermite-Pade polynomials of type I for an arbitrary tuple of $m+1$ formal power series $[f_0,dots,f_m]$, $mgeq1$, about $z=0$ ($f_jin{mathbb C}[[z]]$) under the assumption that the series have a certain (`general
position) nondegeneracy property. This algorithm is a straightforward extension of the classical Viskovatov algorithm for construction of Pade polynomials (for $m=1$ our algorithm coincides with the Viskovatov algorithm). The algorithm proposed here is based on a recurrence relation and has the feature that all the Hermite-Pade polynomials corresponding to the multiindices $(k,k,k,dots,k,k)$, $(k+1,k,k,dots,k,k)$, $(k+1,k+1,k,dots,k,k),dots$, $(k+1,k+1,k+1,dots,k+1,k)$ are already known by the time the algorithm produces the Hermite-Pade polynomials corresponding to the multiindex $(k+1,k+1,k+1,dots,k+1,k+1)$. We show how the Hermite-Pade polynomials corresponding to different multiindices can be found via this algorithm by changing appropriately the initial conditions. The algorithm can be parallelized in $m+1$ independent evaluations at each $n$th step.
Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint He
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We introduce and analyze some numerical results obtained by the authors experimentally. These experiments are related to the well known problem about the distribution of the zeros of Hermite--Pade polynomials for a collection of three functions $[f_0
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